Prediction of performance evolution in learning a determinist trajectory

4*4 grid Minimum period 7 transition Supposing you start in the main cycle Memory and learning strategy getting better with the levels

for (level in seq(1,30,1)) {
  if (level >20) {
    lambda = 1
  } else {
    if (level<5) {
      lambda = level/10
    } else {
      lambda = level/20 + 0.25
    }
    
  }
  performance = data.table(x=seq(0,25,1), y=c(rep(0.25,7),sapply(seq(0,18,1), function(x) { return(sigmoid(x, c(0.6+level/100, lambda, 13-(level*0.5))) * 0.75 + 0.25) } )))
  toPlot = ggplot(performance, aes(x=x,y=y)) + geom_point()
  print(toPlot)
}

Prediction of performance evolution in general rule condition

4*4 grid Minimum period 7 transition Supposing you start in the main cycle Memory and learning strategy getting better with the levels

for (level in seq(1,30,1)) {
  if (level >20) {
    lambda = 5
  } else {
    if (level<5) {
      lambda = level/5
    } else {
      lambda = 5*level/20
    }
    
  }
  performance = data.table(x=seq(0,25,1), y=sapply(seq(0,25,1), function(x) { return(sigmoid(x, c(1, lambda, 12-(level*0.2))) * 0.75 + 0.25) } ))
  toPlot = ggplot(performance, aes(x=x,y=y)) + geom_point()
  print(toPlot)
}